Jamming and percolation of dimers in restricted-valence random sequential adsorption

A P Furlan,Robert M Ziff,Diogo C Dos Santos,Ronald Dickman

doi:10.1103/physrevresearch.2.043027

A P Furlan, Robert M Ziff + Show 2 more

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https://doi.org/10.1103/physrevresearch.2.043027

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Abstract

Restricted-valence random sequential adsorption~(RSA) is studied in its pure and disordered versions, on the square and triangular lattices. For the simplest case~(pure on the square lattice) we prove the absence of percolation for maximum valence $V_{\rm max}=2$. In other cases, Monte Carlo simulations are used to investigate the percolation threshold, universality class, and jamming limit. Our results reveal a continuous transition for the majority of the cases studied. The percolation threshold is computed through finite-size scaling analysis of seven properties; its value increases with the average valency. Scaling plots and data-collapse analyses show that the transition belongs to the standard percolation universality class even in disordered cases

Highlights

Percolation [1] is characterized by the formation of a spanning cluster in a system composed of elements, each present independently with probability p
Random sequential adsorption (RSA) [2,14] is a stochastic process consisting in irreversible deposition of immobile objects onto an initially empty substrate such that each object excludes a certain area from further occupation
We study RSA of dimers on a regular lattice under the restriction that the number of dimers that can attach to a vertex cannot exceed Vmax

Summary

Introduction

Percolation [1] is characterized by the formation of a spanning cluster in a system composed of elements (sites and/or bonds), each present independently with probability p. The probability of a spanning or percolating cluster is only nonzero for p > pc, the percolation threshold, marking a continuous phase transition with associated critical exponents [2,3,4]. A realization of RSA stops when no further deposition events are possible, at which point the system is said to be jammed. Introducing a deposition attempt rate (per unit area, or per site, on a lattice) of unity, a time can be associated with each deposition event in a given realization.

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